This note. The purpose of the present note is to discuss the accuracy of the classifier obtained by minimizing the [1]} convex potential function \(\phi ^\star .\) 
Our main observation is that, for a simple learning problem corresponding to a certain “clean” data distribution \({\cal D}_2\)  that is linearly separable with a margin, minimizing \(\phi ^\star \)  over all bounded-norm linear combinations of base features even when there is no random classification noise only yields a binary classifier with an error rate of 1/2. Since, as shown by [1]}, \(\phi ^\star \)  is the unique strong RCN-robust relaxed convex potential function, this means that minimizing any strong RCN-robust convex potential function in this noise-free scenario may only yield a binary classifier with an error rate of 1/2,
which can be obtained through random guessing.
